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Talk:Introductory mathematics
Not introductory and other issues First of all, the claim that 'Believe it or not the basis of all of mathematics is nothing more than the simple "Next" function." Is not correct, since axioms are the basis of all mathematics. Many objects in maths do not even use explicit numbers, or addition. Additionally, I do not understand the change of notation from "successor" to "Next". It is just confusing, and since it is an introductory article is not helpful, however I will refer to it as "Next" from now on. Numbers Addition specifically over the naturals is defined as calling the Next function, not in general. The sentence about subtraction leading to an ability to write 1 - 3 = x is confusing. The absolute value function appears misplaced here, and looks like it should be a definition of integers and not a definition of the absolute value function, especially when in an introductory article we should not expect a reader to understand notation like this. Multiplication is only defined as repeated addition over the naturals, since it does not make sense for any other number set. How can you add 2 to itself -4 times? The inverse is also introduced immediately without giving any of the properties of multiplication. Division by zero is in general undefined, but to say it is "undefinable" is incorrect since the derivative assigns a value to many 0/0 situations. To say multiplication and addition are fast, but division is slow "even for computers" is also incorrect, as it will depend on the size of the numbers. Division is generally harder for humans, but a computer will not care. Again, exponentiation over the naturals is defined as repeated multiplication. Also, it is not that \sqrt{2} cannot be a rational number, it is that it simply is not a rational number. Also, 0^0 is generally undefined, but usually defined to be 1. Infinity " When a quantity, like the charge of a single electron, becomes so small that it is insignificant we, quite justifiably, treat it as though it were zero.". This is simply not true, and is not justifiable at all. The next sentence implies that the charge of an electron is infinitesimal, despite it having a well defined quantity, and when compared to some other numbers is giant in magnitude. Introducing the infinitesimal in an introductory article also does not make sense, especially when it does not belong to even the real set of numbers, and definitely not the integers or naturals. A differential form of charge is not q \cdot 1/\infinity . " Likewise when a quantity becomes so large that a regular finite quantity becomes insignificant then we call it infinite." Numbers can be arbitrarily large or small, so this again does not make sense. The mass of the ocean may be large, but it is certainly not infinite, and then saying that the mass of the galaxy is the mass of the ocean multiplied by infinity does not make sense either. Introducing the hyperreal numbers at this stage, for introductory mathematics is not helpful for learners, as they will be confused. They have not even been introduced to the real set yet, let alone the real set union some other parts. There are some further issues in the article that I would also like to fix, such as formatting and other parts of the article, however I would love some discussion with the author of the article so I may better understand their position. Horep (talk) 02:17, June 11, 2019 (UTC)